Algebra II with Trigonometry
The Algebra II lessons in the Home Study Companion series are based on Paul A. Foerster's Algebra and Trigonometry: Functions and Applications. This textbook is available as part of Prentice Hall's Classics series, or in older editions through various used book sources (e.g. try Amazon.com). Homeschool parents can order teachers' manuals and solution manuals from Prentice Hall theough their "Oasis" program. The text is a true classic!
Paul A. Foerster has taught mathematics at Alamo Heights High School in San Antonio, Texas since 1961. In that same year he received his teaching certificate from Texas A&M University. His B.S. degree in Chemical Engineering and M.A. degree in Mathematics are from the University of Texas. Among many honors, he was awarded the Presidential Award for Excellence in Mathematics Teaching in 1983. He brings to his teaching and textbook writing the insights from his engineering background. His textbooks contain some of the best collections of real-world applications to be found in any algebra textbook.
The topics covered in this course include Functions and Relations, Systems of Linear Equations and Inequalities, Quadratic Functions and Relations, Higher Degree Polynomials, Complex Numbers, Exponential and Logarithmic Functions, Rational Algebraic Functions, Irrational Algebraic Functions, Sequence and Series, Probability, Data Analysis, and an Introduction to Trigonometry.
Whether or not parents feel comfortable with this material themselves, the students would benefit by being introduced to these topics by an experienced teacher. That is what these video lessons provide. The lessons cover not only new techniques, but new levels of problem solving skills and new models for thinking about practical problems mathematically. All the topics learned in Algebra I are deepened and put into an expanded context. This level of material cannot simply be "presented": it must be taught.
Where appropriate the text introduces computer programming problems to extend pencil and paper solutions and to better approximate real-world scale problems. The Math Without Borders DVD illustrates solutions of the programming problems using spreadsheet programming. Spreadsheets are a good, transparent way to lay out many kinds of programming solutions. The spreadsheet programs covered here can be created using Microsoft Excel (available commercially) or equally well using the spreadsheet component of the free, open source program suite, Open Office. (The programming solutions shown on the disk are done in Open Office, but saved in a format that can be opened with either Open Office or Excel.)
The lessons for this course are distributed on a single DVD ROM, are based on "screen-capture video" technology. To the user they appear as "whiteboard lectures" (see screenshot below).
You will need to separately purchase a copy of Foerster's Algebra and Trigonometry: Functions and Applications. The lessons are based on the Prentice Hall Classics version, but there are only minor differences between this and earlier versions. These may be obtained from Pearson-Prentice Hall, Amazon.com, or elsewhere.
A number of parents have asked how to pace of the class over the course of a school year. In a home schooling environment the schedule can, and probably should, be more flexible than in a standard classroom. The ultimate basis for setting the pace is the level of understanding of the student. This text is designed to be a 1-year course, but I know some people spread it out over two years. The ability and readiness of the student should be the determining factor.
Mathematics textbooks are generally structured on the assumption of covering one section per day, with extra days for testing, review, and re-teaching of the more difficult topics. The table below should help. If you typically cover 1 section per day you would have 38 extra days in a 185 day school year. I would recommend spending 2-3 days for the final word-problem section of each chapter. The problems that are worked out on the videos would be a reasonable selection of problems to assign. If more practice is needed you could select additional odd numbered problems, whose answers are in the back of the text.
I highly recommend that parents be closely involved with the students' progress. The surest way to get behind is to allow students to "slip through" the material without demonstrating that they understand it thoroughly. When this happens early in the course, you will find them unprepared for the work later in the course.
For testing, you could use the Chapter Review and/or Chapter Test sections found at the end of each chapter, or you could pick a selection of easier and harder problems from each section of the chapter. You should always insist that all the work be shown on the same page as the answers. If your students say they can do the problems in their head, ask them to show you on paper what is going on in their head. If they insist that it is a one-step mental problem, have them explain their reasoning to you. I recommend treating this as a practical rather than a moral issue, although you will have to find your own balance on that question.